again we conclude that it must be that:
we can continue in the same fashion untill we get to the last two equations namely:

--->

after substituting the solution for in the last equation we get that

so the final solution is:

now let's consider the case in which :

we can immediately notice that the first two equations became linearly dependent, what this means to us is that now we have less constraints than unknown variables which in turn means that one of the variables can have arbitrary value, and because arbitrary value is just that any number --> we will have infinite number of solutions.

now as we look at the remaining equations we can see that every variable from to vanishes and we are left with the last equation: